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The concept of stability of quasi\u2010static paths used here is essentially a continuity property relatively to the size of the initial perturbations (as in Lyapunov stability) and to the smallness of the rate of application of the external forces (which plays here the role of the small parameter in singular perturbation problems). The discussion of stability is preceded by the presentation of mathematical formulations (plus existence and uniqueness results) for those dynamic and quasi\u2010static problems, in a form that is convenient for the subsequent discussion of stability.<\/jats:p>","DOI":"10.1002\/zamm.200510315","type":"journal-article","created":{"date-parts":[[2007,3,27]],"date-time":"2007-03-27T12:21:12Z","timestamp":1174998072000},"page":"303-313","source":"Crossref","is-referenced-by-count":12,"title":["On the stability of quasi\u2010static paths for finite dimensional elastic\u2010plastic systems with hardening"],"prefix":"10.1002","volume":"87","author":[{"given":"J.A.C","family":"Martins","sequence":"first","affiliation":[]},{"given":"M.D.P","family":"Monteiro Marques","sequence":"additional","affiliation":[]},{"given":"A.","family":"Petrov","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2007,3,27]]},"reference":[{"key":"e_1_2_1_2_2","unstructured":"H.Br\u00e9zis Op\u00e9rateurs maximaux monotones et semi\u2010groupes de contractions dans les espaces de Hilbert North\u2010Holland Mathematics Studies No. 5 Notas de Matem\u00e1tica (50) (North\u2010Holland Publishing Co. Amsterdam 1973)."},{"key":"e_1_2_1_3_2","doi-asserted-by":"crossref","unstructured":"G.DuvautandJ.L.Lions Inequalities in mechanics and physics Grundlehren der Mathematischen Wissenschaften 219 translated from the French by C. W. John (Springer\u2010Verlag Berlin 1976).","DOI":"10.1007\/978-3-642-66165-5"},{"key":"e_1_2_1_4_2","unstructured":"J.Krej\u010d\u00ec Hysteresis Convexity and Dissipation in Hyperbolic Equations (Gakkotosho Tokyo 1996)."},{"key":"e_1_2_1_5_2","doi-asserted-by":"crossref","unstructured":"B.Loret F.Sim\u00f5es andJ.A.C.Martins Flutter instability and ill\u2010posedness in solids and fluid\u2010saturated porous media in: Material Instabilities in Elastic and Plastic Solids (Udine 1999) edited by H. Petryk CISM Courses and Lectures Vol. 414 (Springer Vienna 2000) pp. 109\u2013207.","DOI":"10.1007\/978-3-7091-2562-5_3"},{"key":"e_1_2_1_6_2","doi-asserted-by":"crossref","unstructured":"J.A.C.Martins M.D.P.Monteiro Marques andA.Petrov A report on the stability of quasi\u2010static paths for finite dimensional elastic\u2010plastic systems with hardening Relat\u00f3rio ICIST Vol. DTC 1\/2007 (Instituto Superior T\u00e9cnico Lisboa Portugal 2007).","DOI":"10.1002\/zamm.200510315"},{"key":"e_1_2_1_7_2","unstructured":"J.A.C.Martins F.M.F.Sim\u00f5es A.Pinto da Costa andI.Coelho Three examples on \u201c(in)stability of quasi\u2010static paths\u201d (submitted) (2004)."},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1002\/mma.707"},{"key":"e_1_2_1_9_2","doi-asserted-by":"crossref","unstructured":"R.O'Malley Jr. Singular Perturbation Methods for Ordinary Differential Equations Applied Mathematical Sciences Vol. 89 (Springer\u2010Verlag New York 1991).","DOI":"10.1007\/978-1-4612-0977-5"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.1997.5673"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0045-7825(97)00163-1"},{"key":"e_1_2_1_12_2","doi-asserted-by":"crossref","unstructured":"A.Vasilieva V.Butuzov andL.Kalachev The Boundary Function Method for Singular Perturbation Problems SIAM Studies in Applied Mathematics (SIAM Philadelphia 1995).","DOI":"10.1137\/1.9781611970784"},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.1088\/1742-6596\/22\/1\/015"},{"key":"e_1_2_1_14_2","unstructured":"E.Zeidler Nonlinear functional analysis and its applications III Variational methods and optimization translated from the German by Leo F. 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